The present invention relates generally to analyzing and searching for information in high-dimensional databases. In particular, related information in a database is partitioned using oriented clusters. Furthermore, the present invention relates to an automated system and method for detecting records in a database that are similar to a user defined target record.
It is often desirable to detect sets of related instances in a database that correspond to related information. Instances of information are represented and stored in a database in the form of a set of data values in a multidimensional space. A dimension in the multidimensional space is a feature that characterizes objects represented by the data values. For example, consider an insurance company""s database containing customer information. Each customer is an object corresponding to an instance in the database that is a customer profile, or data value, in the multidimensional feature space of the database. Each data value is an n-tuple corresponding to an instance of the features: age, sex, height, weight, salary, of the customer as well as the number of cars owned by the customer. The dimensions of the multidimensional feature space are the features that characterize the customer namely the age, sex, salary, of the customer and number of cars owned by the customer.
The problem of clustering is the problem of finding sets of data values in a multidimensional feature space that are close to each other, in the sense of some metric, measure or the like, with respect to a particular subset of dimensions. A particular subset of dimensions is a subset of the features that characterize the objects represented by data values stored in the database, and is thus associated with a subspace in the multidimensional feature space. The clustering problem is a known problem in the database literature, for example D. Fisher, xe2x80x9cKnowledge Acquisition via Incremental Conceptual Clusteringxe2x80x9d, Machine Learning 2(2), 1987; T. Zhang, R. Ramakrishnan and M. Livny, xe2x80x9cBIRCH: An Efficient Data Clustering Method for Very Large Databasesxe2x80x9d, Proceedings of the ACM SIGMOD International Conference on Management of Data, Montreal, Canada, June 1996; R. Ng and J. Han, xe2x80x9cEfficient and Effective Clustering Methods for Spatial Data Miningxe2x80x9d, Proceedings of the 20th International Conference on Very Large Data Bases, Santiago, Chile, 1994, pp. 144-155; and M. Zait and H. Messatfa, xe2x80x9cA Comparative Study of Clustering Methodsxe2x80x9d, FGCS Journal, Special Issue on Data Mining, 1997. The clustering problem has numerous applications that relate to other problems such as segmentation, classification, collaborative filtering/data mining and trend analysis. It is also known that existing algorithm designed to solve the problem of clustering break down in high dimensional feature spaces. The difficulty that arises in high dimensional feature spaces is the inherent sparsity of data values. For example, in the above case when objects represented in the database as customer profiles, there may not be many clusters of customer profiles that are similar (close) with respect to all the features: age, height, weight, sex, salary, number of cars, etc. Thus, when the number of features is high the data may become sparse.
In high dimensional feature spaces, however, only some of the features may be relevant when finding clusters. Therefore, one approach to handling high dimensional feature spaces is to select closely correlated features, project out or ignore the other features, and find clusters in the corresponding subspace (see, for example, R. Kohavi and D. Sommerfield, xe2x80x9cFeature Subset Selection Using the Wrapper Method: Overfitting and Dynamic Search Space Topology,xe2x80x9d Proceedings of the First International Conference on Very Large Data Bases, Santiago, Chile, 1994, pp. 144-155). This approach is problematic, however, as it is difficult to find a single subset of features, i.e. one subspace, in which data values cluster well. In other words, different subsets of data values may cluster better for different subsets of features or subspaces.
The clustering problem has been discussed in the literature of both the statistical and database communities. The emphasis in the statistical community is to find clusters based on precisely defined metrics, while the emphasis in the database community is to produce methods for detecting clusters that work efficiently on large data sets. Two known algorithms for finding clusters in large databases are the BIRCH and CLARANS, see T. Zhang, R. Ramakrishnan and M. Livny, supra, and R. Ng and J. Han, supra.
As explained above, many clustering algorithms do not work efficiently in higher dimensional feature spaces because of the sparsity of the data. In many applications, execution of a clustering algorithm is preceded by feature selection. It is desirable to select particular features so that the data values in the feature space are correlated to each other in the subspace associated with the selected features. Pruning away or projecting out undesirable features reduces the number of uncorrelated features that add noise to the data.
The problem of using traditional feature selection methods is that picking certain features in advance leads to a loss in information. Furthermore, in many data sets, some data values are related with respect to a given set of features and others are correlated with respect other features. Thus, it is often infeasible to prune away or project out too many features without at the same time incurring a substantial loss in information.
In order to illustrate this point, consider the following example. In FIG. 1(a) and FIG. 1(b), two different feature subspaces are illustrated. On each subspace the projection of a set of data values in 3-dimensional feature space is shown. Two patterns of the data emerge: the first pattern corresponds to the cluster 101 of data values in the X-Y plane, while the second pattern corresponds to the cluster 102 of data values in the X-Z plane.
It is advantageous to identify a way of expressing and representing such patterns. Feature pre-selection does not seem an appropriate option, because each feature is relevant to at least one of the clusters. In other words, the xe2x80x9cclosenessxe2x80x9d of data values projected into different subspaces of the 3-dimensional feature space is not uniform with respect to the different features.
In the context of a database of customer profiles that include information about the age, sex, salary, and number of cars, it may be the case that the number of cars owned by a given customer is related in a variety of different patterns depending on whether attention is restricted to customer age or sex or salary or all of the above. Hence, different clusters are found in different subspaces depending on which set of features is considered.
Another problem of using traditional feature selection methods is that clusters are assumed to be aligned with a particular coordinate system. For example, in FIG. 1(a) cluster 101 is assumed to be aligned with the Z-axis, while in FIG. 1(b) cluster 102 is assumed to be aligned with the Y-axis. A more realistic distribution of data values may produce cluster which are oriented along arbitrary subspaces.
It is advantageous to identify a way of expressing and representing clusters along arbitrary orientation. In order to illustrate this point consider the example shown in FIGS. 1(c) and 1(d). In FIG. 1(c) a projected X-Y subspace is illustrated in which cluster 103 is shown oriented along a direction P1, and cluster 101 is shown oriented along direction P2 In FIG. 1(d) a projected X-Y subspace is illustrated in which cluster 013 is shown oriented along a direction P3, and cluster 104 is shown oriented along a direction P4.
In the context of a database of customer profiles that include information about the age, height, weight, sex, salary, and number of cars, it may be the case that information about customers may be related along a direction determined by a particular linear combination of salary and age. Hence, different clusters may be found in different subspaces depending on which (oriented) subspace is considered.
A method of analyzing information in the form of a plurality of data values. The plurality of data values represent a plurality of objects. The plurality of data values are distributed in a data space. A set of features which characterize each of the plurality of objects is identified. The plurality of data values are stored in a database. Each of the plurality of data values corresponds to at least one of the plurality of objects based on the set of features. Ones of the plurality of data values stored in the database are partitioned into a plurality of clusters. A respective orientation associated with a position in data space of data values which are contained in each respective cluster of the plurality of clusters is calculated based on the set of features.